Question

A 2kg mass slides down an inclined plane of 27 degrees from top to bottom in 3 seconds. Assuming the coefficient of friction between the two surfaces is 0.48, calculate all the force components including friction and determine the length of the ramp.

Present your answer with a vector diagram.

Present each component of your answer.

Answer 1

Find the x-component of mg:

$$(mg)_x=mg\sin27°=8.90\text{ N}.$$

Find the normal force N:

$$N=N_y=(mg)_y=mg\cos27°=17.5\text{ N}.$$

Find the force of friction:

$$f=f_x=\mu N=8.40\text{ N}.$$

Find the acceleration:

$$a=\frac{F_\text{net}}{m},\\\space\\ F_\text{net}=f-(mg)_x=-0.50\text{ N},\\\space\\ a=-0.25\text{ m/s}^2.$$

The length of the ramp:

$$L=\frac{|a|t^2}{2}=1.125\text{ m}.$$